1) Field of the Invention
The invention relates to devices that teach the relationship between a cylinder's surface areas and volume, its diameter and radius, the top circle circumference and area, the arc length, the sector area, the volume of a slice, the front area of the slice and the side area of the slice.
Across the nation, schools are going through a major reform in their math and science curriculum to bring education standards up to par. The facts show that there is an achievement gap between blacks and whites in mathematics and science. In 1999, when the latest National Assessment of Education Progress (NAEP) test was administered, large differences remained between average scores for blacks and Hispanics on the one hand, versus whites and Asians on the other. Nationally, the achievement gap did not narrow at all during the 1990s. In reading and math, gaps separating poor and minority students from others actually widened at most grade levels and remained the same or dropped only slightly at others (The Education Trust). By the end of grade 4, African American, Latino and poor students of all races are already about two years behind other students. By the time they reach grade 8, they are about three years behind. By the time they reach grade 12, if they do so at all, minority students are about four years behind other young people. The mathematics and science skills of 17-year-old African American and Latino students are similar to those of 13-year-old white students. African Americans and Latinos obtain college degrees at only half the rate of white students. The partnerships between government agency, industry, academia and private organizations are trying to address these issues along with many others. This invention provides a method for teaching the geometric concepts of a cylinder and the equations involved.
2) Prior Art
The prior art consists of teaching the theory and equations for the geometry of a cylinder and its parts. Lessons primarily consist of a mathematical explanation for the following: 1) The circumference of a circle C=πD or C=2πr, 2) The area of a circle A=πr2, 3) The arc length=2πrθ/360, 4) The sector area=πr2θ/360, 5) The volume of a cylinder=πr2L, 6) The volume of a slice=πr2Lθ/360, 7) The front surface area of a cylinder is 2πrL, 8) The front surface area of a slice=2πrLθ/360, 9) And the side surface area of a slice=rL.
The present invention, as distinguished from the prior art, provides a device that clearly demonstrates the relationship between a cylinder, its diameter and radius, the arc length, the sector area, the volume of a slice, the front area of the slice and the side area of the slice. None of the prior art uses a device or tool that includes a hollow outer half-cylinder, and a solid inner half-cylinder that can rotates around a common center for both the inner and outer half-cylinders. And none of the prior art contains individual slices that can be attached to the inner half cylinder to complete a full 360 degrees cylinder.